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ON CLASSES OF EQUIVALENCE AND IDENTIFIABILITY OF AGE-DEPENDENT BRANCHING PROCESSES.

Rui Chen1, Ollivier Hyrien1

  • 1University of Rochester.

Advances in Applied Probability
|January 20, 2015
PubMed
Summary

This study investigates the identifiability of age-dependent branching processes, crucial for biological data analysis. We found that while some models are not identifiable, those with gamma-distributed lifespans are, offering clearer insights into population dynamics.

Keywords:
Bellman-Harris ProcessIdentifiabilitySevastyanov ProcessSmith-Martin process

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Area of Science:

  • Mathematical Biology
  • Stochastic Processes
  • Statistical Modeling

Background:

  • Age-dependent branching processes are vital tools in biological data analysis.
  • The identifiability of these statistical models, crucial for parameter estimation, remains understudied.
  • Understanding model identifiability is key to reliable biological data interpretation.

Purpose of the Study:

  • To investigate the identifiability of age-dependent branching processes.
  • To partition these processes into equivalence classes based on population size distribution.
  • To provide a framework for assessing the identifiability of offspring and lifespan distributions.

Main Methods:

  • Partitioning families of age-dependent branching processes into equivalence classes.
  • Analyzing the distribution of population size within these classes.
  • Examining specific parametric families, including Markov processes and processes with gamma-distributed lifespans.

Main Results:

  • Identified equivalence classes for age-dependent branching processes where population size distribution is identical.
  • Demonstrated that certain Markov processes within this family are not identifiable.
  • Proved that age-dependent processes with gamma-distributed lifespans are identifiable.
  • Showed that Smith-Martin processes are not consistently identifiable.

Conclusions:

  • The identifiability of age-dependent branching processes can be rigorously studied by partitioning them into equivalence classes.
  • Specific model choices, such as gamma-distributed lifespans, ensure identifiability, enhancing their utility in biological modeling.
  • The findings clarify the conditions under which these stochastic models yield unique parameter estimates from observed data.